Two coordinate systems shown separately in a) and b), that we used for descriptions of toroidal magnetic field configurations. Cross sections of our toroid’s surface (with major and minor radii, R₀ and r₀, respectively) with the xz plane are shown with the thick circles. Our toroid has a circular axis at in the z = 0 plane; cross sections of this circular axis with the xz plane indicate two symmetric crosses (outside the origin). A common coordinate of the systems is ϕ, a usual azimuthal angle in the xy plane; it is ϕ = 0 for the half-plane (x> 0)z and ϕ = π for the half-plane (x< 0)z, as labelled in the figure. a) Toroidally curved cylindrical coordinates have r and θ coordinates, in addition. The r coordinate defines toroidal surfaces, which have circular axes identical with our toroid; cross sections of one of these surfaces with the xz plane are shown with thin circles; it is r = r₀/ 2. The θ coordinate is a positional angle. b) Toroidal coordinates have μ and η coordinates, in addition. The μ coordinate defines toroidal surfaces, which have co-centric, but different circular axes lying in the z = 0 plane. The circular axes tend to an asymptotic axis, which fulfills x² + y² = a². Its cross sections with the xz plane are shown with two symmetric bullets at the x axis. The surface of our toroid is defined as μ = μ₀, coshμ₀ = R₀/r₀. Cross sections of a toroidal surface defined by μ = 2μ₀ with the xz plane are shown with thin solid circles. The coordinate η defines spherical surfaces with centers at the z axis. Cross sections of three spherical surfaces (η = ± π/ 4,π/ 4 − π) with the xz plane are plotted as arcs by the dashed line. The absolute value of the coordinate η of a point is a viewing angle under which the asymptotic circular axis is seen (it is demonstrated in the figure; the viewing angle is drawn by the dotted-dashed line and its value is η = π/ 4).